Results 21 to 30 of about 1,868 (82)

On the one‐dimensional polynomial, regular, and regulous images of closed balls and spheres

Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.
Abstract We present a full geometric characterization of the one‐dimensional (semialgebraic) images S$S$ of either n$n$‐dimensional closed balls B¯n⊂Rn$\overline{{\mathcal {B}}}_n\subset {\mathbb {R}}^n$ or n$n$‐dimensional spheres Sn⊂Rn+1${\mathbb {S}}^n\subset {\mathbb {R}}^{n+1}$ under polynomial, regular, and regulous maps for some n⩾1$n\geqslant 1$
José F. Fernando
wiley   +1 more source

The Moment Problem for Continuous Positive Semidefinite Linear functionals

, 2012
Let $\tau$ be a locally convex topology on the countable dimensional polynomial $\reals$-algebra $\rx:=\reals[X_1,...,X_n]$. Let $K$ be a closed subset of $\reals^n$, and let $M:=M_{\{g_1, ... g_s\}}$ be a finitely generated quadratic module in $\rx$. We
C. Berg, C. Berg, C. Berg, E.K. Haviland, E.K. Haviland, Ebrahim Samei, J.B. Lasserre, J.B. Lasserre, J.L. Krivine, M. Putinar, Mehdi Ghasemi, S. Kuhlmann, Salma Kuhlmann   +12 more
core   +1 more source

On the size of the fibers of spectral maps induced by semialgebraic embeddings [PDF]

, 2015
Let ${\mathcal S}(M)$ be the ring of (continuous) semialgebraic functions on a semialgebraic set $M\subset{\mathbb R}^m$ and ${\mathcal S}^*(M)$ its subring of bounded semialgebraic functions.
Fernando, Jose F.
core   +1 more source

A Jordan–Chevalley decomposition beyond algebraic groups

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract We prove a decomposition of definable groups in o‐minimal structures generalizing the Jordan–Chevalley decomposition of linear algebraic groups. It follows that any definable linear group G$G$ is a semidirect product of its maximal normal definable torsion‐free subgroup N(G)$\mathcal {N}(G)$ and a definable subgroup P$P$, unique up to ...
Annalisa Conversano
wiley   +1 more source

Approximation by piecewise-regular maps

, 2019
A real algebraic variety W of dimension m is said to be uniformly rational if each of its points has a Zariski open neighborhood which is biregularly isomorphic to a Zariski open subset of R^m. Let l be any nonnegative integer. We prove that every map of
Bilski, Marcin, Kucharz, Wojciech
core   +1 more source

Expansions of the real field by open sets: definability versus interpretability [PDF]

, 2008
An open set U of the real numbers R is produced such that the expansion (R,+,x,U) of the real field by U defines a Borel isomorph of (R,+,x,N) but does not define N.
Friedman, H., Kurdyka, K., Miller, C., Speissegger, P.   +3 more
core   +9 more sources

On Rainbow Turán Densities of Trees

Random Structures &Algorithms, Volume 66, Issue 3, May 2025.
ABSTRACT For a given collection 𝒢=(G1,…,Gk) of graphs on a common vertex set V$$ V $$, which we call a graph system, a graph H$$ H $$ on a vertex set V(H)⊆V$$ V(H)\subseteq V $$ is called a rainbow subgraph of 𝒢 if there exists an injective function ψ:E(H)→[k]$$ \psi :E(H)\to \left[k\right] $$ such that e∈Gψ(e)$$ e\in {G}_{\psi (e)} $$ for each e∈E(H)$$
Seonghyuk Im, Jaehoon Kim, Hyunwoo Lee, Haesong Seo   +3 more
wiley   +1 more source

Outer Lipschitz classification of normal pairs of Hölder triangles

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract A normal pair of Hölder triangles is the union of two normally embedded Hölder triangles satisfying some natural conditions on the tangency orders of their boundary arcs. It is a special case of a surface germ, a germ at the origin of a two‐dimensional closed semialgebraic (or, more general, definable in a polynomially bounded o‐minimal ...
Lev Birbrair, Andrei Gabrielov
wiley   +1 more source

New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker, Tong Jin, Oliver Lorscheid   +2 more
wiley   +1 more source

Data‐driven methods for quantitative imaging

GAMM-Mitteilungen, Volume 48, Issue 1, March 2025.
Abstract In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly important in medical imaging applications, such as quantitative magnetic resonance imaging (qMRI), where quantitative maps of biophysical parameters can characterize ...
Guozhi Dong, Moritz Flaschel, Michael Hintermüller, Kostas Papafitsoros, Clemens Sirotenko, Karsten Tabelow   +5 more
wiley   +1 more source